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2D Geometry: Chapter Questions
1. What are some of the special relationships between angles?
2. What are perimeter and circumference and how are they relevant in daily life?
3. How is the formula for area of a parallelogram related to area of a rectangle?
4. How is the formula for area of a triangle related to area of a rectangle?
5. How do you find the area of irregular shapes?
6. How do you find the area of shaded regions?
2D Geometry: Chapter Problems
Determining if a Triangle is Possible
Classwork
1. Determine if triangles can be formed with the following side lengths:
a. 4 m, 12 m, 15 m
b. 8 yd, 5 yd, 13 yd
c. 7 in, 15 in, 23 in
d. 24 ft, 35 ft, 58 ft
e. 18 cm, 27 cm, 46 cm
2. Which of the following sets of angles could form a triangle?
a. 45°, 57°, 78°
b. 90°, 54°, 26°
c. 104°, 90°, 34°
d. 55°, 91°, 105°
e. 56°, 45°, 79°
3. Predict the length of the third side of a triangle whose known sides are lengths:
a. 5 in, 23 in
b. 7 m, 32 m
c. 8 in, 12 in
d. 12 cm, 15 cm
e. 43 yd, 57 yd
Homework
4. Determine if triangles can be formed with the following side lengths:
a. 7 m, 11 m, 17 m
b. 13 yd, 9 yd, 23 yd
c. 13 in, 23 in, 36 in
d. 5 ft, 23 ft, 29 ft
e. 27 cm, 35 cm, 46 cm
5. Which of the following sets of angles could form a triangle?
a. 52°, 37°, 95°
b. 107°, 39°, 34°
c. 112°, 90°, 68°
d. 52°, 94°, 108°
e. 48°, 53°, 79°
6. Predict the length of the third side of a triangle whose known sides are lengths:
a. 8 in, 37 in
b. 17 m, 26 m
c. 12 in, 25 in
d. 9 cm, 18 cm
e. 82 yd, 99 yd
Special Pairs of Angles
Classwork
7. If two angles have the same measure are they congruent?
8. Angle 1 and Angle 2 are complementary. If ∠1 has a measure of 420 what would
the measure of ∠2 be?
9. Determine the measure of the unknown angle A in the figure below.
10. What is the complement of 720?
11. If Angle 1 measures 480 and Angle 2 measures 420 are these angles
complementary?
12. Angle R and S are supplementary. If Angle R measures 1150 what is the measure
of Angle S?
13. What is the measure of Angle A?
14. What is the supplement of 720?
15. If Angle X measures 530 and Angle Y measures 1270 are these angles
supplementary?
16. What is the complement of 680? Supplement?
17. Using what you know about vertical angles, find the measure of the missing angles.
You must be able to explain why.
Angle
Measurement
Reason
∠𝐴
65°
Given
18.
Parallel lines m and n are cut by a transversal l. If
∠𝐵
the measure of angle 5 is 37o determine the measures of
the remaining angles. You must be able to explain why.
∠𝐶
∠𝐷
Angle
Measurement
Reason
∠1
∠2
∠3
∠4
∠6
∠7
∠8
Homework
19. Angle M has a measure of 360 and Angle N has a measure of 240. Are these two
angles congruent?
20. Angle r and Angle s are complementary. If ∠𝑠 has a measure of 260 what would be
the measure of ∠𝑟?
21. Determine the measure of the unknown angle A in the figure below.
22. What is the complement of 90?
23. If Angle x measures 530 and Angle y measures 1270 are these angles
complimentary?
24. Angle A and B are supplementary. If ∠𝐴 measures 970 what is the measure of ∠𝐵?
25. What is 𝑚∠𝐴?
26. What is the supplement of 90?
27. If 𝑚∠1 =480 and 𝑚∠2 = 420 are these angles supplementary?
28. What is the complement of 840? Supplement?
29. Using what you know about vertical angles, find the measure of the missing angles.
You must be able to explain why.
30. Parallel lines m and n are cut by a transversal l. If the measure of angle 5 is 680
determine the measures of the remaining angles. You must be able to explain why.
Perimeter and Circumference
Classwork
Find the perimeter of each figure.
31.
32.
33.
34.
35. Determine the circumference of a circle with radius 5 cm.
36. Determine the circumference of a circle with radius 2.3 m.
37. Determine the circumference of a circle whose diameter is 8 m.
38. Determine the circumference of a circle whose diameter is 24.6 cm.
39. What is the diameter of a circle whose circumference is 47.1 m?
Homework
Find the perimeter of each figure.
40.
41.
42.
43.
44. Determine the circumference of a circle whose radius is 3.5 m.
45. Determine the circumference of a circle whose radius is 32 inches.
46. Determine the circumference of a circle whose diameter is 32 inches.
47. Determine the circumference of a circle with diameter 8 feet.
48. What is the radius of a circle whose circumference is 13.188 cm?
Rectangles & Parallelograms
Classwork
Find the area of each figure.
49.
50.
51.
52.
53.
54. The length of a rectangle is 10 in and the width is 3 in. What is its area?
55. How do you find the area of a rectangle?
56. How do you find the area of a parallelogram?
57. What is true of the base and height of a parallelogram?
58. What is the base of a parallelogram whose height is 4 cm and whose area is 44
cm2?
Homework
Find the area of each figure.
59.
60.
61.
62.
63.
64. The length of a rectangle is 17 m and the width is 6 m. What is its area?
65. How do you find the area of a rectangle?
66. How do you find the area of a parallelogram?
67. What is true of the base and height of a parallelogram?
68. What is the base of a parallelogram whose height is 7 cm and whose area is 63
cm2?
Triangles & Trapezoids
Classwork
Find the area of each figure.
69.
70.
71.
72.
73.
74. Find the height of a triangle whose area is 20 in2 and whose base is 8 in.
Homework
Find the area of each figure.
75.
76.
77.
78.
79.
80. Find the height of a triangle whose area is 25 in2 and whose base is 5 in.
Circles
Classwork
Find the area of each figure.
81.
82.
83. A goat is tied to a 5 m rope. What is the area of the grass he can eat?
84. What is the area of a circle with a radius of 7 cm?
85. What is the area of a circle with a diameter of 16 yd?
86. How do you find area of a circle when given radius?
Homework
Find the area of each figure.
87.
88.
89. A circular sprinkler has a radius of 4 m. How much grass can the sprinkler water?
90. What is the area of a circle with a radius of 5 in?
91. What is the area of a circle with a diameter of 14 m?
92. How do you find area of a circle when given diameter?
Irregular Figures
Classwork
Find the area of each figure.
93.
94.
95.
96.
Homework
Find the area of each figure.
97.
98.
99.
100.
Shaded Figures
Classwork
Find the area of each shaded region..
101.
102.
103.
Homework
Find the area of each shaded region.
104.
105.
106.
2 Dimensional Geometry – Unit Review
Multiple Choice– Choose the correct answer for each question. No partial credit will be
given.
1. Determine which set of sides cannot be used to form a triangle.
a. 8 in, 9 in, 15 in
b. 15 m, 27 m, 41 m
c. 9 yd, 9 yd, 17 yd
d. 4 ft, 9 ft, 13 ft
2. If an angle measures 90, what is the measure of its vertical angle?
a. 90
b. 180
c. 270
140
x
d. 360
3. ABC measures 62. Its complementary angle measures:
a. 28
b. 62
c. 208
d. 298
4. How can this angle be classified?
a. Acute
b. Right
c. Obtuse
d. Straight
5. What is the perimeter of an equilateral triangle with 6-inch sides?
a. 18 inches
b. 24 inches
c. 27 inches
d. 36 inches
6. A soccer field has a length of 100 yards and a width of 60 yards. What is the
perimeter of the field?
a. 160 yards
b. 220 yards
c. 320 yards
d. 6000 square yards
7. What is the area of a rectangle with length 36 cm and width 4 cm?
a. 72 cm
b. 144 cm
c. 144 cm2
d. 72 cm2
8. What is the area of the figure pictured to the
right?
a. 6 square units
b. 10 square units
c. 12 square units
d. 50 square units
9. A triangle has an area of 36 yd2 and a base of 3 yd, what is the height of the
triangle?
a. 12 yd
b. 24 yd
c. 108 yd
d. 324 yd
10. Find the area of the figure to the right.
a. 17 cm2
b. 20 cm2
c. 27 cm2
d. 36 cm2
11. Find the height of the parallelogram with a length of 50 in and an area of 275 in 2.
a. 5.5 in
b. 22 in
c. 5.5 in2
d. 11 in
12. Jewell wants to tile her kitchen floor with tiles that are 1.5 ft2. If her kitchen is 18 ft by
12 ft, how many tiles will she need?
a. 40
b. 144
c. 216
d. 324
13. Find the area of the figure to the right.
a. 44 cm
b. 44 cm2
c. 54 cm2
d. 32 cm2
14. Find the area of the shaded region to the right.
a. 20 cm2
b. 40 cm2
c. 80 cm2
d. 120 cm2
15. Find the length of the base of a triangle with an area of 20 cm 2 and a height of 5
cm.
a. 4 cm
b. 8 cm
c. 15 cm
d. 100 cm
Short Constructed Response – Write the correct answer for each question.
16. A circular carpet covers an area of 201 cm2. What is the radius of the carpet?
_________
17. What is the diameter of a circle whose area is 38.04 in2?
d=
__________
18. In order to decorate for a party, you need to cover 3 rectangular tables with
tablecloth. The tables measure 36 in by 72 in. If you want 2 inches overhang on
each side, how many square inches of fabric would it take to cover the 3 tables?
__________
19. The doors in your home need to be painted. Each door measures 8 ft x 3 ft. You are
amazed that you have 22 doors to paint! A can of paint can cover 400 square feet.
How many cans of paint will you need to purchase?
__________
20. A diagram of the side of your shed is below. How much siding is needed to cover
both sides of the shed that are shaped as pictured?
__________
Extended Constructed Response - Solve the problem, showing all work. Partial credit
may be given.
21. Your parents have offered to pay you to wallpaper the kitchen walls. The wallpaper
that you want costs $12/square foot. The rectangular kitchen measures 16 ft x 12 ft,
with a height of 8 ft. One doorway measures 8 ft x 3 ft and two windows measures 3
ft x 5 ft.
a. Calculate the area of the kitchen walls, pretending there are no windows or
doorways .
b. What is the area of the kitchen walls, when the doorways and windows are
taken into account?
c. What will be the minimum cost to wallpaper the kitchen?
22. You have been asked to design a flower garden with an area of 52 ft2. The client
has no preference for the shape of the garden. It’s all up to you!
a. If it will cost $3/ft to put flowers in the garden, determine the total cost.
b. Provide two possible dimensions of the flower garden.
c. Identify the shape that has the smallest perimeter.
23. A decorator wants to install two picture windows, measuring 12 ft. x 8 ft. The
windows will be placed on a wall measuring 72 ft x 12 ft.
a. What is the area of the wall, without windows?
b. How much area will two windows cover?
c. Wallpaper, costing $6/square foot, will be purchased to cover the wall,
once the windows are installed. What will be the least amount of money
spent on the wallpaper?
24. A bag of grass seed can cover 120 square feet. Ms. Peabody wants to seed her
front and back yard. The front yard is rectangular in shape, measuring 10 ft x 8 ft.
Her back yard has an irregular shape and is pictured below.
A. Calculate the square footage of Ms. Peabody’s front yard.
B. Calculate the square footage of Ms. Peabody’s back yard.
C. How many bags of grass seed will Ms. Peabody need to purchase?